An Introductory Study on Time Series Modeling and Forecasting (1302.6613v1)

Abstract: Time series modeling and forecasting has fundamental importance to various practical domains. Thus a lot of active research works is going on in this subject during several years. Many important models have been proposed in literature for improving the accuracy and effectiveness of time series forecasting. The aim of this dissertation work is to present a concise description of some popular time series forecasting models used in practice, with their salient features. In this thesis, we have described three important classes of time series models, viz. the stochastic, neural networks and SVM based models, together with their inherent forecasting strengths and weaknesses. We have also discussed about the basic issues related to time series modeling, such as stationarity, parsimony, overfitting, etc. Our discussion about different time series models is supported by giving the experimental forecast results, performed on six real time series datasets. While fitting a model to a dataset, special care is taken to select the most parsimonious one. To evaluate forecast accuracy as well as to compare among different models fitted to a time series, we have used the five performance measures, viz. MSE, MAD, RMSE, MAPE and Theil's U-statistics. For each of the six datasets, we have shown the obtained forecast diagram which graphically depicts the closeness between the original and forecasted observations. To have authenticity as well as clarity in our discussion about time series modeling and forecasting, we have taken the help of various published research works from reputed journals and some standard books.

• The paper introduces foundational time series modeling techniques, comparing ARIMA, neural networks, and SVMs across varied real-world datasets.
• It employs robust evaluation metrics such as MSE, MAD, RMSE, MAPE, and Theil’s U to measure predictive performance.
• The findings reveal superior non-linear capturing by ANNs and SVMs, paving the way for future exploration of hybrid forecasting approaches.

An Introductory Study on Time Series Modeling and Forecasting

Overview

The document presents a scholarly investigation into the field of time series modeling and forecasting. It encompasses a comprehensive examination of several prevalent methodologies, highlighting their application in various domains such as economics, finance, and engineering. The work is methodically structured to introduce foundational concepts before exploring stochastic models, artificial neural networks (ANNs), and support vector machines (SVMs), each with their intrinsic forecasting strengths and limitations.

Stochastic Models

The paper commences with an exploration of stochastic models, notably the Autoregressive Integrated Moving Average (ARIMA) and its variations such as SARIMA and ARFIMA. These models pivot on the Box-Jenkins methodology for identifying and estimating optimal model parameters. Despite their popularity, these models assume a linear relationship within the data, which can be restrictive in capturing complex patterns inherent in real-world datasets.

Neural Networks

The document transitions to neural networks, underscoring their non-linear modeling capabilities. ANNs, particularly multi-layer perceptrons, are acclaimed for their data-driven nature, enabling them to model intricate patterns without explicit statistical preconceptions. Variants such as Time Lagged Neural Networks (TLNN) and Seasonal ANNs (SANN) offer tailored solutions for specific time series challenges, such as accounting for seasonal effects without preprocessing steps like differencing.

Support Vector Machines

The analysis then addresses Support Vector Machines, which extend their application from classification to regression (SVR) and time series prediction. SVMs leverage structural risk minimization, providing robust generalization by maximizing margins in transformed feature spaces. The document further explores enhancements like Least Square SVM (LS-SVM) and Dynamic LS-SVM (DLS-SVM), emphasizing computational efficiency and dynamic adaptability.

Numerical Results

Experiments conducted on six real datasets, ranging from the Canadian lynx time series to the monthly U.S. accidental deaths dataset, reveal the varying efficacy of these methods. The performance metrics include MSE, MAD, RMSE, MAPE, and Theil’s U-statistics, each offering insights into the predictive accuracy and computational practicality of the models. Notably, the results exhibit that while traditional stochastic models like ARIMA perform adequately, ANNs and SVMs demonstrate superior capabilities in capturing non-linear trends in several instances.

Implications and Future Directions

The implications of this paper are manifold. Practically, the diversity in model selection caters to a wide array of applications, influencing strategic decision-making processes across industries. Theoretically, the comparative analysis fosters a deeper understanding of the strengths and limitations inherent to each modeling approach.

Looking forward, the integration of hybrid models that amalgamate the strengths of various methodologies promises enhanced forecasting precision. The document hints at future exploration into ensemble techniques, which could mitigate the limitations of individual models and harness complementary strengths to further refine time series forecasting.

In conclusion, this paper serves as a substantive guide for researchers and practitioners alike, elucidating the nuanced landscape of time series modeling while providing empirical insights to guide future research endeavors.